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The Paradox of Infinity

  1. Apr 22, 2003 #1
    What is infinity? How can something infinite expand? Once and for all, how can we conclude that the universe is infinite? The fact that the universe is infinite may contradict brane theory. Consequently, could it be tenable to suggest that this brane is a subuniverse?
    Of course, the idea of an infinite universe could just be based on the inifite boundary theory proposed by Stephen Hawking.
     
  2. jcsd
  3. Apr 23, 2003 #2
    I feel it important, nay nessesary, to point out, right before this discussion begins that....

    Infinity is NOT a number.

    It is NOT a number.

    Thank you. Please bear this in mind.
     
  4. Apr 23, 2003 #3
    Majin, you should perhaps have posted this in the Philosophy Forum.

    Infinity is the concept of something that goes on forever.

    Something infinite cannot expand (IMO).

    We can never conclude that the universe is infinite, beyond question.

    No, branes are not "sub-universes". Branes are mathematical additions of dimensions (AFAIK).
     
  5. Apr 23, 2003 #4
    Without meaning to be insulting, but how can someone not yet able to manipulate equations claim to be able to reason about brane theory?
     
  6. Apr 23, 2003 #5

    drag

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    What's all this talk about infinity being
    paradoxical, all the time? What's so paradoxical
    about it ? (I guess this should indeed be in the
    philosophy forum.)

    What's paradoxical about expanding infinity ?

    Live long and prosper.
     
  7. Apr 23, 2003 #6
    I knew I should've put this is in the philosophy forum! *slaps head* tsk, tsk.

    Anyhow, infinity is paradoxical because, as Mentat pointed out, something infinite is unable to expand. It goes on, and on, forever so how can something infinite expand?
     
  8. Apr 23, 2003 #7
    I'm working on it. Any how, I love doing math, because its just like a logic problem, and I love those too.

    plus, what you said was not insulting. The truth is never,AFAIK, insulting.
     
  9. Apr 24, 2003 #8

    drag

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    Greetings !
    Well, if it's only spacial expansion for example
    then the distances between all objects will
    simply grow.

    Do understand me people - I'm not, at the moment,
    denying the concept of real infinity as having
    its own paradox of some kind, but I have yet
    to see any clear fomalization of such a paradox.

    Live long and prosper.
     
  10. Apr 24, 2003 #9
    What/who are you talking about?
     
  11. Apr 24, 2003 #10
    No, no, I was talking about the idea that the spacial dimensions themselves are expanding, not just that things are getting farther apart.
     
  12. Apr 24, 2003 #11
    Something infinite can expand.

    Consider the set of the numbers A = {1, 2, 3, ......}, and now consider the set of A and 1/2, so it is B := {1/2, 1, 2, 3, 4, 5, 6, 7, ..}.

    Then there is one number in B which is not in A. This could be said to be an expansion of A.

    This I believe is a counterexample to one of Mentat's ascertations:

    'Something infinite cannot expand',

    although he needs say more precisely what he means by this.
     
  13. Apr 24, 2003 #12
    This infinity talk remindes me of cardinality, countable, and uncountable sets. It's a really cool topic in mathematical analysis. In a sense, not all infinities are equal, i.e., not all sets with infinite number of elements can be enumerated. For instance, the interval (0,1) or any finite interval on the real line is larger than the set of all integers.
     
  14. Apr 25, 2003 #13

    drag

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    Greetings !
    That IS what I meant. Plus gives an appropriate
    example here.

    For example, suppose that you draw coordinates
    and assign a number to every area of specific
    size. Then multiply your infinite set of areas
    by 2 and you'll see that the amount of areas
    is now twice the previous amount - between say
    your house and the nearest store.

    It may be conceptually difficult, but if you
    consider that space is infinite you don't have
    to worry about what's outside at all - simply
    don't bother yourself with that thought.
    (I must note that I find it difficult, at this time,
    to think of a more solid formalization of this idea,
    so perhaps there is a fundumental mistake of some
    kind in this line of reasoning.)

    Live long and prosper.
     
  15. Apr 25, 2003 #14
    Alright, let me explain: I am not talking about mathematical infinities. I know that there can be more than one infinity, in maths, and that there can be "bigger" infinities. However, I'm talking about space itself. If you take a space that is infinite (as in, having no end), how could you possibly add more space to this? Even if you could, (though I don't think you could) your result would be the same as before (infinity), and thus you haven't made it any bigger at all.
     
  16. Apr 25, 2003 #15

    drag

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    Well, I wasn't talking about math, just using
    it as an example. The question is - what's the
    difference ? Is there any ? And why ?

    Live long and prosper.
     
  17. Apr 25, 2003 #16
    If it is already infinite, it can't quite get bigger. Infinity is having no end, eternal. Infinity describes endlessness in the whole so you can't add anything to it.
     
  18. Apr 25, 2003 #17

    dav2008

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    ok ok ..right...BUT ..did you see that example?

    Take all even numbers...you would agree that there are an infinite amount of them....But you can always add an odd number to that set of inifinite numbers...just like "plus" said...

    Its more mathematical in that sense...not physical..
     
  19. Apr 25, 2003 #18
    Yes, I know that in mathematics infinity can be added with another infinity and the sort. BUT, my question is in the physical sense. We can't run away from the physical world.
     
  20. Apr 25, 2003 #19
    I believe that what separates the mathematical universe from the physical universe is practicality. Practicality tells us that in order to exist, the universe must have physical laws. These laws (speed of light, for example) impose finite barriers in an attempt to give order to the universe. Even though these laws do prevent many physical infinities (max speed, min temp, etc), the fact that the universe is in constant motion creates many new infinities.

    A common infinity is the coastline of great britain. It is impossible to obtain an exact answer for this, for to do so one must measure at increments infinitely less than planck length, which would require so much energy as to warp space enough to disrupt their results. Not to mention the uncertainty principle...

    This is not to say that Britain does not have a definite coastline at a specific increment of time. It does, yet practicality (that word again) prevents us from saying so, because WE cannot obtain this measurement. The physical universe has a human element to it that the mathematical universe lacks. Einstein said that "Only two things are infinite: the universe and human stupidity, and I'm not sure about the former." So perhaps the universe is finite, and humans are so infinitely stupid that they cannot comprehend this.

    Perhaps this thread belongs in the "philosophy" forum, but oh well.
     
  21. Apr 26, 2003 #20
    Yes, maybe I should ask a moderator to move this thread to philosophy.

    Anyway, you bring up an excellent point that has been neglected. Although, it occurs to me that the concept of human stupidity being the obstacle of our understanding of the universe seems be undefined. I came upon this conclusion on the premise that everything is relative. If you were traveling at c, the external world would become blue shifted. But to an external observer, you are the one who is blue shifted. So, you, and the observer are both correct for the whole matter is anisotropic and each of you has the right to your observations. Now, from our perspective, the universe is infinite. Possibly, to an "external" observer, the universe, perhaps, is not infinite. I doubt stupidity has anything to do with the matter.
     
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